A. Adamu, C.E. Chidume, D. Kitkuan, P. Kumam, Geometric inequalities for solving variational inequality problems in certain Banach spaces

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DOI: 10.23952/jnva.7.2023.2.07

Volume 7, Issue 2, 1 April 2023, Pages 267-278

Abstract. In this paper, we develop some new geometric inequalities in p-uniformly convex and uniformly smooth real Banach spaces with $p>1$ . We use the inequalities as tools to obtain the strong convergence of the sequence generated by a subsgradient method to a solution that solves fixed point and variational inequality problems. Furthermore, the convergence theorem established can be applicable in, for example, $L_p(\Omega)$ , where $\Omega\subset R$ is bounded set and $l_p(R)$ for $p\in(2,\infty)$ . Finally, numerical implementations of the proposed method in the real Banach space $L_5([-1,1])$ are presented.

How to Cite this Article:
A. Adamu, C.E. Chidume, D. Kitkuan, P. Kumam, Geometric inequalities for solving variational inequality problems in certain Banach spaces, J. Nonlinear Var. Anal. 7 (2023), 267-278.